The Mixture of Autoregressive Hidden Markov Models of Morphology for Dentritic Spines During Activation Process

Abstract

The dendritic spines play a crucial role in learning and memory processes, epileptogenesis, drug addiction, and postinjury recovery. The shape of the dendritic spine is a morphological key to understand learning and memory process. The classification of the dendritic spines is based on their shapes but the major questions are how the shapes changes in time, how the synaptic strength changes, and is there a correlation between shapes and synaptic strength? Because the changes of the classes by dendritic spines during activation are time dependent, the forward-directed autoregressive hidden Markov model (ARHMM) can be used to model these changes. It is also more appropriate to use an ARHMM directed backward in time. Thus, the mixture of forward-directed ARHMM and backward-directed ARHMM (MARHMM) is used to model time-dependent data related to the dendritic spines. In this article, we discuss (1) how to choose the initial probability vector and transition and dependence matrices in ARHMM and MARHMM for modeling the dendritic spines changes and (2) how to estimate these matrices. Many descriptors to classify dendritic spines in twodimensional or/and three-dimensional (3D) are available. Our results from sensitivity analysis show that the classification that comes from 3D descriptors is closer to the truth, and estimated transition and dependence probability matrices are connected with the molecular mechanism of the dendritic spines activation.

Cooperativity, information gain, and energy cost during early LTP in dendritic spines

“…Our model is based on the assumption that a dendritic spine can be treated as the system with discrete states, which is compatible with some morphological observations (Bourne and Harris 2008; Montgomery and Madison 2004; Bokota et al 2016; Urban et al 2020). In this respect, it is similar in architecture to some previous discrete models of synapses or dendritic spines (Fusi et al 2005; Leibold and Kempter 2008; Barrett et al 2009; Benna and Fusi 2016).…”

“…entropy production rate, equivalent to plasticity energy rate, is ill-defined and yields infinities for unidirectional transitions). In contrast, our model takes as a basis well defined morphological synaptic states, with bidirectional transitions between them that are estimated based on empirical data (Bokota et al 2016; Basu et al 2018; Urban et al 2020). The latter feature, i.e., bidirectional transitions, makes our model thermodynamically consistent (with finite entropy production), as was explained in a previous model of metabolic molecular activity in a single spine within the framework of cascade models of learning and memory (Karbowski 2019).…”

“…Empirical data indicate that a single dendritic spine can be regarded as a four state stochastic system with well defined morphological (mesoscopic) states (Montgomery and Madison 2004; Bokota et al 2016; Basu et al 2018; Urban et al 2020; Fig. 1A).…”

“…Generally, we take the following form of the transition matrix : where is the intrinsic basic transition rate between and s i at spine i , and it is independent of the neighboring synapses. These intrinsic rates are the same for each i , setting the temporal scale for basal synaptic plasticity, and they were estimated based on data in (Urban et al 2020) and are presented in Table 1. The symbol d ( s i ) is the spine size at state s i of spine i and it is proportional to spine surface area (see Appendix A), whereas θ ( x ) denotes the sign function of the argument x , where θ ( x ) = 1 if x ≥ 0, and θ ( x ) = −1 if x < 0.…”

Modeling Dinophysis in Western Andalucía using an autoregressive hidden Markov model

“…Autoregressive HMMs on the other hand, were initially developed for speech recognition ( Juang and Rabiner 1986 , 1985 ). They have since been applied to various issues in recent years ( Urban et al 2020 ; Bartolucci et al 2014 ; Shannon and Byrne 2010 ), but have not been used to model algae.…”